Requirements for fission

mitch_1211

So I think, as a rule of thumb that for fission to be possible [itex]\frac{Z^2}{A}[/itex][itex]\geq[/itex]47

I want to be able to derive this relationship though..

If a nucleus deforms into an ellipsoid, its surface area can be described by

4[itex]\pi[/itex]R²(1+[itex]\frac{2}{5}[/itex][itex]\epsilon^2[/itex] + ...) call this X

And its Coulomb energy can be described as

[itex]\frac{3Z^2}{20\pi\epsilon_0R}[/itex](1-[itex]\frac{1}{5}[/itex][itex]\epsilon^2[/itex] + ...) call this Y

And so ΔBE = X-Y

For fission to occur set ΔBE ≤ 0

Once I've done all this I'm not sure how to get ΔBE in terms of A and Z only. I know R = r₀A^1/3

thanks

mitch_1211

I should mention that [itex]\epsilon[/itex] is an arbitrary deformation parameter associated with the ellipsoid and can be factored out

mfb

You can use that formula for R and solve for ##\frac{\partial (X-Y)}{\partial \epsilon}=0##.
I would expect that this overestimates the required Z^2/A - if that derivative is negative, the nucleus should not form at all or decay within less than a femtosecond.